• Title/Summary/Keyword: hyperbolic

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Upper Boundary Line Analysis of Rice Yield Response to Meteorological Condition for Yield Prediction I. Boundary Line Analysis and Construction of Yield Prediction Model (최대경계선을 이용한 벼 수량의 기상반응분석과 수량 예측 I. 최대경계선 분석과 수량예측모형 구축)

  • 김창국;이변우;한원식
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.46 no.3
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    • pp.241-247
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    • 2001
  • Boundary line method was adopted to analyze the relationships between rice yield and meteorological conditions during rice growing period. Boundary lines of yield responses to mean temperature($T_a$) and sunshine hour( $S_{h}$) and diurnal temperature range($T_r$) were well-fitted to hyperbolic functions of f($T_a$) =$$\beta$_{0t}$(1-EXP(-$$\beta$_{1t}$ $\times$ ($T_a$) ) and f( $S_{h}$)=$$\beta$_{0t}$((1-EXP($$\beta$_{1t}$$\times$ $S_{h}$)), to quadratic function of f($T_r$) =$\beta$$_{0r}$(1-($T_r$ 1r)$^2$), respectively. to take into account to, the sterility caused by low temperature during reproductive stage, cooling degree days [$T_c$ =$\Sigma$(20-$T_a$] for 30 days before heading were calculated. Boundary lines of yield responses to $T_c$ were fitted well to exponential function of f($T_c$) )=$\beta$$_{0c}$exp(-$$\beta$_{1c}$$\times$$T_c$ ). Excluding the constants of $\beta$$_{0s}$ from the boundary line functions, formed are the relative function values in the range of 0 to 1. And these were used as yield indices of the meteorological elements which indicate the degree of influence on rice yield. Assuming that the meteorological elements act multiplicatively and independently from each other, meteorological yield index (MIY) was calculated by the geometric mean of indices for each meteorological elements. MIY in each growth period showed good linear relationship with rice yield. The MIY's during 31 to 45 days after transplanting(DAT) in vegetative stage, during 30 to 16 days before heading (DBH) in reproductive stage and during 20 days after heading (DAH) in ripening stage showed greater explainablity for yield variation in each growth stage. MIY for the whole growth period was calculated by the following three methods of geometric mean of the indices for vegetative stage (MIVG), reproductive stage (HIRG) and ripening stage (HIRS). MI $Y_{I}$ was calculated by the geometric mean of meteorological indices showing the highest determination coefficient n each growth stage of rice. That is, (equation omitted) was calculated by the geometric mean of all the MIY's for all the growth periods devided into 15 to 20 days intervals from transplanting to 40 DAH. MI $Y_{III}$ was calculated by the geometric mean of MIY's for 45 days of vegetative stage (MIV $G_{0-45}$ ), 30 days of reproductive stage (MIR $G_{30-0}$) and 40 days of ripening stage (MIR $S_{0-40}$). MI $Y_{I}$, MI $Y_{II}$ and MI $Y_{III}$ showed good linear relationships with grain yield, the coefficients of determination being 0.651, 0.670 and 0.613, respectively.and 0.613, respectively.

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Calculation of Unit Hydrograph from Discharge Curve, Determination of Sluice Dimension and Tidal Computation for Determination of the Closure curve (단위유량도와 비수갑문 단면 및 방조제 축조곡선 결정을 위한 조속계산)

  • 최귀열
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.7 no.1
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    • pp.861-876
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    • 1965
  • During my stay in the Netherlands, I have studied the following, primarily in relation to the Mokpo Yong-san project which had been studied by the NEDECO for a feasibility report. 1. Unit hydrograph at Naju There are many ways to make unit hydrograph, but I want explain here to make unit hydrograph from the- actual run of curve at Naju. A discharge curve made from one rain storm depends on rainfall intensity per houre After finriing hydrograph every two hours, we will get two-hour unit hydrograph to devide each ordinate of the two-hour hydrograph by the rainfall intensity. I have used one storm from June 24 to June 26, 1963, recording a rainfall intensity of average 9. 4 mm per hour for 12 hours. If several rain gage stations had already been established in the catchment area. above Naju prior to this storm, I could have gathered accurate data on rainfall intensity throughout the catchment area. As it was, I used I the automatic rain gage record of the Mokpo I moteorological station to determine the rainfall lntensity. In order. to develop the unit ~Ydrograph at Naju, I subtracted the basic flow from the total runoff flow. I also tried to keed the difference between the calculated discharge amount and the measured discharge less than 1O~ The discharge period. of an unit graph depends on the length of the catchment area. 2. Determination of sluice dimension Acoording to principles of design presently used in our country, a one-day storm with a frequency of 20 years must be discharged in 8 hours. These design criteria are not adequate, and several dams have washed out in the past years. The design of the spillway and sluice dimensions must be based on the maximun peak discharge flowing into the reservoir to avoid crop and structure damages. The total flow into the reservoir is the summation of flow described by the Mokpo hydrograph, the basic flow from all the catchment areas and the rainfall on the reservoir area. To calculate the amount of water discharged through the sluiceCper half hour), the average head during that interval must be known. This can be calculated from the known water level outside the sluiceCdetermined by the tide) and from an estimated water level inside the reservoir at the end of each time interval. The total amount of water discharged through the sluice can be calculated from this average head, the time interval and the cross-sectional area of' the sluice. From the inflow into the .reservoir and the outflow through the sluice gates I calculated the change in the volume of water stored in the reservoir at half-hour intervals. From the stored volume of water and the known storage capacity of the reservoir, I was able to calculate the water level in the reservoir. The Calculated water level in the reservoir must be the same as the estimated water level. Mean stand tide will be adequate to use for determining the sluice dimension because spring tide is worse case and neap tide is best condition for the I result of the calculatio 3. Tidal computation for determination of the closure curve. During the construction of a dam, whether by building up of a succession of horizontael layers or by building in from both sides, the velocity of the water flowinii through the closing gapwill increase, because of the gradual decrease in the cross sectional area of the gap. 1 calculated the . velocities in the closing gap during flood and ebb for the first mentioned method of construction until the cross-sectional area has been reduced to about 25% of the original area, the change in tidal movement within the reservoir being negligible. Up to that point, the increase of the velocity is more or less hyperbolic. During the closing of the last 25 % of the gap, less water can flow out of the reservoir. This causes a rise of the mean water level of the reservoir. The difference in hydraulic head is then no longer negligible and must be taken into account. When, during the course of construction. the submerged weir become a free weir the critical flow occurs. The critical flow is that point, during either ebb or flood, at which the velocity reaches a maximum. When the dam is raised further. the velocity decreases because of the decrease\ulcorner in the height of the water above the weir. The calculation of the currents and velocities for a stage in the closure of the final gap is done in the following manner; Using an average tide with a neglible daily quantity, I estimated the water level on the pustream side of. the dam (inner water level). I determined the current through the gap for each hour by multiplying the storage area by the increment of the rise in water level. The velocity at a given moment can be determined from the calcalated current in m3/sec, and the cross-sectional area at that moment. At the same time from the difference between inner water level and tidal level (outer water level) the velocity can be calculated with the formula $h= \frac{V^2}{2g}$ and must be equal to the velocity detertnined from the current. If there is a difference in velocity, a new estimate of the inner water level must be made and entire procedure should be repeated. When the higher water level is equal to or more than 2/3 times the difference between the lower water level and the crest of the dam, we speak of a "free weir." The flow over the weir is then dependent upon the higher water level and not on the difference between high and low water levels. When the weir is "submerged", that is, the higher water level is less than 2/3 times the difference between the lower water and the crest of the dam, the difference between the high and low levels being decisive. The free weir normally occurs first during ebb, and is due to. the fact that mean level in the estuary is higher than the mean level of . the tide in building dams with barges the maximum velocity in the closing gap may not be more than 3m/sec. As the maximum velocities are higher than this limit we must use other construction methods in closing the gap. This can be done by dump-cars from each side or by using a cable way.e or by using a cable way.

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